We start with an assumption that natural numbers 1, 2, etc. are known, order among them is established (i.e. we know which one follows the other and is greater than the previous) and an operation of addition among them is well defined. So, for every pair of natural numbers (say, 5 and 8) an operation of addition (denoted by a plus sign between these two numbers) is defined and result of this operation of addition in a known natural number (5 + 8 = 13). We also assume that sometimes an operation of subtraction is also defined for two natural numbers (e.g. 8 - 5 = 3) but it is defined only if we subtract a smaller number from a bigger one. From a syntactical standpoint we can define these operations in many different ways. Say, ADD(5, 8) = 13 or SUBTRACT(8,5) = 3 or 5 @ 8 = 13 or in any other way. Using a plus or a minus signs is just a tradition. The approach employed here to more rigorously define integer numbers is one of many that can be used by those who understand the need for strict definitions of mathematical concepts. It is syntactical in nature (we used strings to represent numbers) and similar approach will be used to define rational and complex numbers.